1. Field of the Invention
The present invention relates to the field of digital signal processing, and more particularly to a digital-to-analog conversion using a time based pulse width to ensure a known and unchanging relationship between the input digital word and a resultant sine wave amplitude.
2. Description of Related Art
Digital-to-analog conversion is the process of converting digital codes into a continuous range of analog signals. Analog-to-digital conversion is the complementary process of converting a continuous range of analog signals into digital codes. These conversions are important to interface real-world systems, which typically monitor continuously varying analog signals, with digital systems that process, store, interpret, and manipulate the analog values.
The resolution of a digital-to-analog converter is the smallest change in the voltage that can be detected by the system and that can produce a change in the digital code. The resolution determines the total number of digital codes, or quantization levels, that will be recognized or produced by the converter. The resolution of the D/A converter is usually specified in terms of the bits in the digital code or in terms of the least significant bit (LSB) of the system. An n-bit code allows for 2.sup.n quantization levels. As the number of bits increases, the step size between quantization levels decreases, therefor increasing the accuracy of the system when a conversion is made between an analog and digital signal.
Digital codes are typically converted to analog voltages by assigning a voltage weight to each bit in the digital code and then summing the voltage weights of the entire code. A typical digital converter consists of a network of precision resistors, input switches, and level shifters to activate the switches to convert a digital code to an analog current or voltage.
Digital converters commonly have a fixed or variable reference level. The reference level determines the switching threshold of the precision switches that form a controlled impedance network, which in turn controls the value of the output signal. Fixed reference digital converters produce an output signal that is proportional to the digital input. Multiplying digital converters produce an output signal that is proportional to the product of a varying reference level times a digital code.
An example of the applications for digital to analog converters is presented herein to illustrate the benefits of the present invention. Hemispherical resonator gyroscopes are known in the art for measuring an angular rate of a body about a predetermined axis. HRGs are of critical importance in space applications, such as the orienting of satellites and space vehicles. HRGs are reliable and have a long active life, making the gyro especially suited for this purpose. The gyros are typically comprised of a forcer electrode assembly, a hemispherical thin-walled quartz shell, and a pick-off electrode assembly joined together with a rare-earth metal such as indium. The unit is housed in a vacuum chamber with electrical feeds to communicate voltage signals from the gyro to a microprocessor for interpretation. The general operation of the gyroscope is discussed in the Letters Patent to Loper, Jr. et al., U.S. Pat. No. 4,951,508, which is fully incorporated herein by reference.
The hemispherical resonator 10 is a bell-shaped thin walled structure with a rim that can be made to deform from a circular profile to an elliptical profile when subjected to certain external electrical fields. The resonator is supported by an integral stem which itself is supported by the housing for the pick-off and forcer electrodes. By applying a cyclical forcing voltage, a standing wave pattern can be established in the resonator. To establish the standing wave, the hemispherical resonator is initially biased at a voltage of known magnitude, and then a varying electrical field is applied at the forcer electrodes. If the forcer electrodes apply the appropriate varying electrical field at angular intervals of 90 degrees, the resonator will flexure in a standing wave such as that shown in FIG. 1.
The primary harmonic resonating wave has four nodes a,b,c,d and four antinodes e,f,g,h around the perimeter of the resonator, alternating and equal spaced forty-five degrees apart. Nodes are points on the standing wave where displacement is a minimum, and antinodes are points on the standing wave where displacement is a maximum. Operation of the HRG requires precise tracking of the standing wave movement, which in turn requires that the location of the nodes and antinodes be accurately determined.
It is a physical property of the gyroscope that if an unrestrained resonator is rotated about an axis normal to the page (see FIG. 2), the standing wave will precess in an opposite direction to the original rotation due to Coriolis force. Moreover, the amount of the angular precess will be 0.3 times the angular displacement of the resonator, where 0.3 is a geometric property of the resonator's hemispherical shape and holds constant for any rotation angle and any rotation rate. For example, if the resonator of FIG. 1 is rotated ninety degrees in the counter-clockwise direction, as indicated by the angular displacement of the notch 20, the standing wave will precess twenty-seven degrees clockwise as shown in FIG. 2. In this manner when an HRG is rotated about its primary axis, by measuring the change in the angular position of the standing wave information about the rotation of the HRG can be determined.
The position of the standing wave both before and after the rotation of the gyroscope is determined by the pick-off electrodes positioned about the external annular component of the housing. By measuring the capacitance across the gap formed between the pick-off electrodes and the resonator, the distance across the gap can be accurately determined. This information is processed by a microprocessor in a manner such that the exact position of the standing wave is determined. By measuring the change in position of the standing wave, the rotation of the gyro can readily be determined.
The gyro of the present example employs a rate control loop that uses the rate drive to null the in-phase nodal amplitude component, i.e., standing wave deflection. FIG. 3 is a representation of a rate control loop, where the box 30 represents a model of the HRG mechanics. The model includes a scale factor K which converts volts to an electrostatic force that cancels the coriolis force due to an inertial input, and the resultant difference force to dynamic response P(s) of the in-phase nodal amplitude y.sub.i. The difference force includes a thermal noise component .OMEGA..sub.TN as well as a bias component .OMEGA..sub.B. The input from the HRG pick-off is amplified 40 and converted to a digital signal 50 where a microprocessor 60 can analyze the signal and output a rate estimate R. The digital rate estimate is supplied to the digital to analog converter which generates an HRG phase synchronous signal of the necessary amplitude to maintain Y.sub.i at zero.
The function of the digital-to-analog converter ("DAC") 70 in this example is to change a digital word into an analog voltage or current signal. In this case, the digital word represents the amplitude of the input inertial rate, and the DAC converts the digital word into the representative sine wave equivalent. The output from the DAC supplies the necessary control voltage to maintain the resonant standing wave at null in the presence of inertial forces. Any amplitude error in the sine wave generated by the DAC directly corrupts the estimate of the inertial rate being sensed by the HRG when used in a digital force rebalance control mechanism.
The prior art technique employed to generate the control voltage to maintain the HRG at null is a time-invariant digital-to-analog converter that produces a square wave at the necessary frequency and amplitude. The amplitude of the first harmonic sine wave is known to be 4/.pi. times the square wave amplitude. However, the accuracy of the square wave amplitude is limited by the accuracy of the DAC. A good 12-bit DAC is typically around 49 parts-per-million ("PPM") relative to full scale. This accuracy is insufficient for most HRG applications, so the conventional DAC is factory calibrated to 0.5 PPM (equivalent to a 22-Bit converter). However, the factory calibration starts degrading immediately, and after twelve years in a modest thermal environment, the calibration of the conventional DAC can degrade as much as 25 percent of the uncalibrated level. This results in unacceptable accuracy from the HRG.